Abstract

We propose a hybrid mode-locking scheme for wave-breaking free fiber lasers based on a saturable Bragg reflector and the nonlinear polarization evolution in the fiber section. With this scheme, the self-starting operation is ensured by the saturable Bragg reflector while the nonlinear polarization evolution acts as an additional pulse shaper in the steady state. Owing to the sensitivity of the pulse dynamics to filtering effects, a tuning range of more than 10nm as well as the suppression of undesired modes of operation became possible. The impact of the modulation depth and the non-saturated losses is discussed via comparative measurements with different saturable Bragg reflectors.

1. Introduction

Passively mode-locked fiber lasers were studied intensively during the last decades and became useful light sources for various applications. Passively mode-loked fiber lasers generating parabolic or more general wave-breaking free pulses drawed particular attention as reduced peak intensities inside the resonator offer the possibility to scale up the pulse energy [1,2]. The pulse formation is based on an interplay between positive group-velocity dispersion (GVD) and self-phase modulation (SPM). During propagation in a fiber section or amplifier this interplay leads to optical wave-breaking unless the pulses are reshaped in the nonlinear regime resulting in a self-similar propagation [3]. In a laser the evolution towards wave-breaking is interrupted by filtering effects of the limited gain bandwidth and the mode-locking mechanism, respectively [4]. This is in contrast to the stretched-pulse regime where the self-amplitude modulation (SAM) of the mode-locking mechanism is only needed for the initialization and stabilization of the inherently stable pulses. The steady state itself relies only on the reciprocal phase behaviour of SPM and GVD inside the fibers. In the positive dispersion regime where parabolic and wave-breaking free pulses can be generated, the phase behaviour of SPM and GVD is cumulative which explains the necessity for and sensitivity to (self-) amplitude modulation in the steady-state. Filtering effects can therefore be used to control the output characteristic.

It has been shown that additional amplitude modulation provided by spectral filters leads to a stabilization of the pulse train and dispersion control could be set aside [5]. Even linear filters reduce the influence of the nonlinear polarization evolution (NPE) in the steady state now acting as an additional pulse shaper [6, 7]. The corresponding approach with nonlinear filters (namely saturable absorbers) can additionally stabilize the pulse train during built-up. The utilization of two saturable absorber mechanisms in ultrafast fiber lasers has indeed been discussed in previous publications [8–10] but their interplay in the parabolic pulse and wave-breaking free pulse regime, respectively has, to the best of out knowledge, not been addressed so far.

In this work we investigate the role of saturable Bragg reflectors (SBR) as nonlinear temporal filters implemented in a wave-breaking free fiber laser acting together with the NPE in the fiber section. To point out the role of the SBRs, a comparison with the same oscillator solely mode-locked by NPE has been made. We will demonstrate that the nonlinear characteristic of the SBR strongly influences the pulse build-up leading to an enhanced self-starting capability. Owing to the strong preference for the mode-locked state, a cw-operation of the laser became rather impossible. The hybrid mode-locked laser was tunable over more than 10nm by changing the feedback of the NPE. In addition, the spectral width could be adjusted from 18.5nm to 34 nm. The adjustable nonlinear characteristic allows the suppresion of competitive chaotic pulsation. A short description of some parts of this work was previously reported in [12].

2. Experimental setup

The fiber laser used for our experiments is sketched in Fig. 1 and was also described in previous publications [4, 12, 13]. For the experiments we used different commercial SBRs (Batop GmbH) based on GaAs/AlAs Bragg mirrors and InGaAs quantum wells in front of the mirror implemeted in a sigma-branch. Owing to their non-resonant design, the dispersion slopes are almost flat and negligible. The relaxation time constants of the SBRs were measured by pump-probe technique in a Mach-Zehnder interferometer and the other parameters were taken from the datasheets [14]. The basic data of the AR-coated devices are summarized in Table 1. To overcome their saturation threshold, tight focussing with AR-coated lenses was used. The focal lengths were choosen in a way that all SBRs were operated at a factor of about 6 above their saturation fluence, so the SAM can be regarded as beeing saturated [15]. The comparison with the laser mode-locked by NPE only was realized by replacing the SBR with a highly reflecting mirror.

In order to adjust the polarization state for the NPE in the fiber section (4.8m long single-mode fiber (SMF), 0.14m long highly doped ytterbium gain fiber and 0.44m SMF) wave-plates were applied. The energy exchange between the polarization modes owing to cross-phase modulation leads to an intensity dependent rotation of the polarization state which is transfered into SAM by the polarization beamsplitter behind the fiber section. To change the feedback of the NPE we varied the half wave-plate behind the fiber section (HWP) and the quarter-wave-plate in front of the fiber section (QWP 2) while the quarter wave-plate behind the fiber section (QWP 1) remained fixed [16]. The position of QWP1 was aligned in a way that the polarization state was linear in the central part of the pulse. To control the cavity dispersion, a compressor based on diffraction gratings (900 grooves/mm) was implemented. Throughout the experiments presented here, the cavity dispersion was fixed at 0.015 ps2 which was in center of the dispersion region for stable parabolic pulse operation found without the SBRs [4].

Table 1. Overview about the basic data of the saturable Bragg reflectors.

3. Enhancement of the self-starting capability

In general, the formation of ultrashort pulses results from a continuous shortening of the most intensive mode-beating fluctuations of the free-running laser. The saturable absorber mechanism equalizes the distance between the longitudinal modes which is inter alia inhibited by dispersion and Fabry-Perot effects leading to uneven mode-spacing. The tendency of a laser to self-start can therfore be determined by the correlation time of the modes which characterizes their tendency to loose coherence by random phase pertubations [17].

Krausz et al. proposed a scheme to measure this correlation time τc by observing the 3dB-width of the first RF-beat note and the number of modes present in the free-running laser [17]. The intracavity power P required for self-starting can be related to τc according to
κ·P>1lnm·TRτc
where m is the initial number of modes and κ a constant of the nonlinearity. In a typical fiber laser mode-locked by NPE using 1-m length of fiber, κ≈10-4 W-1. Details how to determine κ for other mode-locking schemes were not given. The correlation time is
τc=1π.1Δv3dB
where Δν3dB is the 3-dB full width of the first beat note in the RF-spectrum. It should be noted that this approach acts on the assumption of zero cavity dispersion and absent Fabry-Perot effects. Nevertheless, the comparison of different mode-locking schemes in the same setup allows for reasonable conclusions about their influence on the mode-locking threshold.

The RF-beat note measured with a resolution bandwidth of 10 Hz and the optical spectrum are shown in Fig. 2(a) and (b) for the SAM-1040-40. The sharp beat note in (a) gives a correlation time of 600µs. The number of modes was estimated at -20 dB to 76,000, whereas we ensured that the intensity of amplified spontaneous emission (measured by blocking the resonator) was at least 5 dB below that level. The number of modes was estimated close to the ASE background as these spectral components can contribute significantly to the duration of the mode beat fluctuation. The number of modes is indeed not exactly determinable but the logarithm of this value changes the result only slightly. A similar behaviour was also oberserved with the other SBRs and the results are summarized in Table 2. For comparison, the measurements of the laser mode-locked only by NPE are displayed in Fig. 2 (c) and (d). The beat note is much broader and the corresponding correlation time is reduced to 150µs. The optical spectrum has indeed a much broader FWHM but the intensity drops down rapidly so that only 11,000 modes have been measured at -20 dB. Assuming κ≈5·10-4 W-1m-1 this corresponds to a intracavity power of about 60mW required for self-starting. The laser starts its mode-locked operation with an output power of 23mW. Taking the required intracavity power of 60mW into account, this corresponds to an output coupling ratio of about 30% which is a small but realistic value for NPE mode-locking.

Fig. 2.(a) First RF-beat note and (b) optical spectrum of the free-running hybrid mode-locked laser with SAM-1040-40. (c) and (d) corresponding measurement of the laser mode-locked by NPE only.

The required power for self-starting with the hybrid mode-locking scheme could not be deduced as κ could not be quantified. However, the minimum κ·P required for self-starting is decreased by nearly one order of magnitude by all SBRs. Consequently the laser produced ultrashort pulses just above laser threshold. Cw-operation could only be found in a very limited range of wave-plate settings and was unstable. Usually, the laser switches either to pulsed operation or runs out within a few seconds. The hysteresis region between cw and pulsed operation which is a characteristic of passively mode-locked fiber lasers vanished completely.

The different behaviour during pulse build-up becomes obvious by recalling that the pulse shortening ratio of a saturable absorber whose net gain window is determined by the pulse energy like an SBR does not depend on the pulse duration. In contrast, the pulse shortening ratio of an artificial saturable absorber based on a Kerr-nonlinearity like the NPE indeed depends on the pulse duration. Therefore, the pulse build-up occurs much slower resulting in a higher mode-locking threshold.

The enhancement of the self-starting capability is beneficial when the absorber action of the NPE is too weak to mode-lock a laser alone. As already mentioned this is a particular problem for oscillators with a large cavity dispersion. To demonstrate this, we set the dispersion control aside and operated the oscillator at a cavity dispersion of 0.167 ps2. The 3 dB-width of the attained spectrum was 4.9nm corresponding to a Fourier-limited pulse duration of 428 fs. In Ref. [18] we also demonstrated mode-locking of an all-fiber version of the proposed setup with a cavity dispersion of 0.15 ps2. In both setups, the initialization of pulsed operation was not possible without the additional amplitude modulation of an SBR.

4. Tuning of the spectral output characteristic

Another advantage of the proposed setup is the tunability of the spectral output resulting from the pulse shaping of the NPE as soon as the steady state is reached. In Fig. 3(a), the stability diagram introduced in Ref. [19] in the plane of the position of HWP and QWP2 (whereas QWP1 was fixed at the same position) is displayed for SAM-1040-30 and SAM-1040-65. The measurement with SAM-1040-40 showed similar stability regions and is not displayed for the sake of clarity. As can be seen, the NPE feedback can be variied over a wide range without leaving the mode-locked state. It is to mention that the mode-locked region also contains small regions with irregular pulse trains. These states depend on various experimental parameters and could not be fully reproduced in subsequent measurements. Therefore, no distinction between regular and irregular pulse trains was drawn in Fig. 3(a). The graph shows also clear hysteresis regions between the mode-locked state and no laser operation. Naturally, self-starting of the laser is not possible in the bistability regions. Cw-operation occurs only in a limited range of wave-plate positions and was unstable as mentioned above. Therefore it could not be resolved in this measurement. It is remarkable that again the modulation depth as well as the non-saturated losses of the SBRs had only minor influence once the laser is mode-locked. Beside the enhancement of the self-starting capability, this is another indication that the SBR is dominant during pulse built-up whereas the steady-state is mainly influenced by the NPE. This conclusion is consistent with observations made in other operating regimes of ultrafast oscillators [8, 11]. In contrast, the stability diagram of the laser mode-locked by NPE only (displayed in Fig. 3(b)) showed only two localized regions of wave-plate settings for mode-locked operation so the potential of tuning the output characteristic was minimal.

The hybrid mode-locked laser could be tuned by changing the feedback of the NPE. In the measurement shown in Fig. 4(a) we varied QWP2 in the setup with SAM-1040-40 and shifted the central wavelength from 1022nm to 1032 nm. Also the spectral FWHM can be adjusted by variing QWP2 as can be seen from Fig. 4(b). In this measurement, HWP and QWP1 were at different positions related to Fig. 4(a) and the FWHM could be tuned from 18.5nm to 34 nm. Other experimental series showed similar tuning ranges. For all settings of the wave-plates, the pulses could be externally dechirped within 10%of the Fourier-limit as known for the parabolic and wave-breaking free regime, respectively [4]. Within the tuning ranges presented, the pulse energy variied between 2 nJ and 3.5 nJ which is due to changed output coupling ratios. In both mode-locking schemes, the obtainable pulse energy was only limited by the available pump power.

Tunability is of particular importance when subsequent amplifier media have only small gain bandwidths like Yb:KGW or Yb:KYW. With the additional SBR the gain of this amplifier media can be utilized completely by adapting the central wavelength as well as the spectral energy density. Another possible applications of tunable fs-pulses is the optimization of the spectral output during supercontinuum generation in microstructured fibers or frequency conversion in nonlinear crystals.

Fig. 3.Stability diagram of the laser in the plane of the positions of the half wave-plate and
the quarter wave-plate 2.

5. Suppression of undesired modes of operation

NPE pulse shaping can not only be used to control the output properties of the pulses but also for the suppression of undesired modes of operation. Parabolic or wave-breaking free pulses are generally unstable against the cw-state before a certain cavity dispersion threshold is exceeded, as theoretically shown in Ref. [20]. The elimination of cw-operation was already mentioned in section 3 and is also underlaid with the fact that the minimum cavity dispersion for stable pulsed operation decreased from 0.010 ps2 to 0.005 ps2 when an SBR was implemeted. Even above this threshold, cw-backgrounds occured in the setup without the SBR which were highly sensitive to many experimental parameters like wavelength dependent coupling into the SMF or losses. These parameters can change by and by owing to mechanical instabilities of the hardware. With the SBR implemented in the cavity these problems vansished and the laser became much more long term stable. Also mechanical or temperature induced disturbances of the fiber section did not affect the mode-locked pulses as much as in the setup without the SBR.

Fig. 5.Transition from bunched noise-like operation to wave-breaking free operation taken with a photonic bandgap fiber for dispersion control by changing the position of QWP2. Single pulse operation corresponds to the lowest spectrum whereas the other corresponds to bunched noise-like pules.

But even within the mode-locked states there are competing regimes. The most trouble-some in the laboratory was the build up of chaotic pulsation without any order structure refered to as bunch noise-like pulse formation. It can be attributed to the combined effect of polarization mode dispersion, gain response and a nonlinear transmission element [21]. Owing to the additional birefringence of a photonic bandgap fiber (PBF) implemented for dispersion control, this mode of operation caused particular trouble [13]. Nevertheless, it occured also in the setup with the grating compressor for intracavity dispersion control.

When the bulky grating compressor was replaced by the 4.05m long piece of PBF (Crystal Fibre A/S HC-1060-02), the roundtrip time was approximately doubled. The initialization of pulsed operation was not possible without the SBR (SAM-1040-40) as the NPE action alone was too weak [7]. The output characteristic of the bunched noise-like pulses is dislayed in Fig. 5 where the top spectrum corresponds to the autocorrelation trace shown in Fig. 6(a). The broad spectrum contains many pulses which were generated and destroyed randomly. This is expressed by the sharp coherence spike apearing on a broad shoulder in the autocorrelation trace indicating incomplete mode-locking. By turning QWP2 this mode of operation can be convicted into wave-breaking free operation shown in Fig. 5 by the lowest spectrum and in Fig. 6(b), respectively. The optical spectrum showed indeed some structure (see Ref. [13] for details) but the chirped as well as the dechirped autocorrelation trace was a Gaussian. No additional pulse was observable even with the long-range autocorrelator (150 ps scanning range) or the fast photodiode/oscilloscope (2GHz resolution). Owing to an optimized feedback of the NPE the bunch of pulses merged together to a single pulse circulating in the resonator.

Fig. 6.Autocorrelation traces taken with a photonic bandgap fiber for dispersion control.

6. Conclusion

In conclusion, we discussed the application of two saturable absorber mechanisms in wave-breaking free fiber lasers at 1µm. The additional saturable Bragg-reflector reduced the mode-locking threshold drastically, stabilized the laser against competitive cw-operation and facilitated the suppression of chaotic pulsations. Based on our results we conclude that the modulation depth and non-saturated loss of the saturable Bragg-reflector has only a minor influence on this behaviour. The nonlinear polarization evolution in the fiber section acts as an additional pulse shaper. Owing to the sensitivity of the pulse evolution in the steady-state this filtering effect can be used to tune the spectral output characteristic. A tuning range from 1022nm to 1032nm has been demonstrated. Also the spectral width could be adjusted from 18.5nm and 34 nm. The tunable oscillator presented here is a versatile fs-light source allowing for spectral adaption to subsequent amplifiers or frequency conversion stages. Strikingly speaking, with the proposed setup one can benefit from the performance of a slow saturable absorber during pulse built-up without loosing the advantages of a fast one in the steady-state.

Acknowledgment

The authors thank Marcel Schultze (Leibniz Universität Hannover, Germany) for measuring the relaxation time constants of our SBRs and the Deutsche Forschungsgemeinschaft (DFG) for their financial support under grant SFB 407.

Transition from bunched noise-like operation to wave-breaking free operation taken with a photonic bandgap fiber for dispersion control by changing the position of QWP2. Single pulse operation corresponds to the lowest spectrum whereas the other corresponds to bunched noise-like pules.